Basic - Trying to understand a probability wave

I'm having a hard time understanding the concept of a probability wave. Let me try to explain myself.

Imagine there is radiation propagating through free space. It has an electric field and a magnetic field oscillating orthogonal to one another as given by Maxwell's equations. It propagates at speed c. Thus I can actually visualize the wave traveling through space at speed c. I could actually get in front of this wave if I could travel faster than c (obviously I can't, I'm not arguing anything close to different...solely saying this for arguments sake). Now if other waves are in free space they will interfere with my wave that is traveling. If this wave goes through a tiny slit it diffracts.

Now what to do with the probability wave?

If I fire an electron through space. I can visualize this particle traveling at some speed. So do I now think of this electron also as a wave? Can I say that look here is a wave traveling through space. But it doesn't have a propagation speed right? I couldn't get in front of it. This is a probability wave, well what does that mean physically. When I take the modulus and square it I get a probability distribution of where this electron exists within a volume. How do I make the distinction between an EM wave and a probability wave?

A huge confusion comes in when we talk about the double slit experiment.

So a probability wave comes through slit one, and a another wave comes through slit two. They interfere with each other and change the probability distribution. So do I visualize these probability waves just like EM waves traveling through the slits?

Any help clarifying these rather elementary quantum ideas would be great. Thank you.